Nonlinear Power Research Articles

JAX-COSMO: An End-to-End Differentiable and GPU Accelerated Cosmology Library

We present jax-cosmo, a library for automatically differentiable cosmological theory calculations. It uses the JAX library, which has created a new coding ecosystem, especially in probabilistic programming. As well as batch acceleration, just-in-time compilation, and automatic optimization of code for different hardware modalities (CPU, GPU, TPU), JAX exposes an automatic differentiation (autodiff) mechanism. Thanks to autodiff, jax-cosmo gives access to the derivatives of cosmological likelihoods with respect to any of their parameters, and thus enables a range of powerful Bayesian inference algorithms, otherwise impractical in cosmology, such as Hamiltonian Monte Carlo and Variational Inference. In its initial release, jax-cosmo implements background evolution, linear and non-linear power spectra (using halofit or the Eisenstein and Hu transfer function), as well as angular power spectra with the Limber approximation for galaxy and weak lensing probes, all differentiable with respect to the cosmological parameters and their other inputs. We illustrate how autodiff can be a game-changer for common tasks involving Fisher matrix computations, or full posterior inference with gradient-based techniques. In particular, we show how Fisher matrices are now fast, exact, no longer require any fine tuning, and are themselves differentiable. Finally, using a Dark Energy Survey Year 1 3x2pt analysis as a benchmark, we demonstrate how jax-cosmo can be combined with Probabilistic Programming Languages to perform posterior inference with state-of-the-art algorithms including a No U-Turn Sampler, Automatic Differentiation Variational Inference,and Neural Transport HMC. We further demonstrate that Normalizing Flows using Neural Transport are a promising methodology for model validation in the early stages of analysis. <em>The software and documentation referred to in this paper can be found <a href="https://github.com/DifferentiableUniverseInitiative/jax-cosmo-paper/">here</a></em>.

Event-triggered model-free adaptive predictive control for multi-area power systems under deception attacks

This paper focuses on the event-triggered model-free adaptive predictive load frequency control (LFC) problem for multi-area power systems under false data injection (FDI) attacks. First, the power system model is assumed to be unknown, and the nonlinear power system is converted into an equivalent linear data model using the input and output data of the powerline system. The FDI attacks on the power system is also modeled, and a Bernoulli stochastic process is used to represent whether the data is transmitted successfully or not. Second, the equivalent linear data model to predicts upcoming events, and a new event-triggered model-free adaptive predictive control scheme is designed via the predictions. And a RBF neural network disturbance estimator is designed to estimate and compensate for the effects caused by disturbances, and then power system stability is analyzed. An event-triggered scheme is also developed in the design of the LFC in order to save communication and computational burden. The results show that the designed control algorithm is data-driven independent of the power system structure and does not require the measurement of any system state signals. Finally, the effectiveness and correctness of the scheme is verified by a three-area numerical example and simulation results.

Improved analytical modeling of the nonlinear power spectrum in modified gravity cosmologies

Reliable analytical modeling of the non-linear power spectrum (PS) of matter perturbations is among the chief pre-requisites for cosmological analyses from the largest sky surveys. This is especially true for the models that extend the standard general-relativity paradigm by adding the fifth force, where numerical simulations can be prohibitively expensive. Here we present a method for building accurate PS models for two modified gravity (MG) variants: namely the Hu-Sawicki $f(R)$, and the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld. We start by modifying the standard halo model (HM) with respect to the baseline Lambda-Cold-Dark-Matter ($\Lambda$CDM) scenario, by using the HM components with specific MG extensions. We find that our $P(k)_{\text{HM}}$ retains 5% accuracy only up to mildly non-linear scales ($k \lesssim 0.3$ $h/\,\mbox{Mpc}$) when compared to PS from numerical simulations. At the same time, our HM prescription much more accurately captures the ratio $\Upsilon(k) = P(k)_{\text{MG}}/P(k)_{\Lambda \text{CDM}}$ up to non-linear scales. We show that using HM-derived $\Upsilon(k)$ together with a viable non-linear $\Lambda$CDM $P(k)$ prescription (such as HALOFIT), we render a much better and more accurate PS predictions in MG. The new approach yields considerably improved performance, with modeled $P(k)_{\text{MG}}$ being now accurate to within 5% all the way to non-linear scales of $k \lesssim 2.5-3$ $h/\,\mbox{Mpc}$. The magnitude of deviations from GR as fostered by these MG models is typically $\mathcal{O}(10\%)$ in these regimes. Therefore reaching 5% PS modeling is enough for forecasting constraints on modern-era cosmological observables.

Energy-aware intelligent scheduling for deadline-constrained workflows in sustainable cloud computing

It is challenging to handle the non-linear power consumption model, complex workflow structures, and diverse user-defined deadlines for energy-efficient workflow scheduling in sustainable cloud computing. Although metaheuristics are very attractive to solve this problem, most of the existing work regards the problem as a black-box and ignores the use of domain knowledge. To make up for their shortcomings, this paper tailors an energy-aware intelligent scheduling algorithm (EIS) with three new mechanisms. First, we derive the optimal execution time that minimizes energy consumption for each task on a given resource. Second, based on the optimal execution time of each workflow task, the EIS distributes the workflow slack time (difference between its completion time and deadline) to reduce the voltages and frequencies of task executions for energy saving. Third, the EIS mines the idle time gaps caused by task precedence constraints to further reduce dynamic energy consumption whilst satisfying workflows’ deadline constraints. To measure the performance of the EIS, we conduct extensive comparison experiments based on actual workflow applications. The results demonstrate that the energy consumption of the EIS is much lower than that of the competitors under different deadlines, and has a faster descend rate with the evolution process.

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed, and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

Some power allocation algorithms for cognitive uplink satellite systems

Cognitive satellite communication (SatCom) is rapidly emerging as a promising technology to overcome the scarcity of the exclusive licensed band model in order to fulfill the increasing demand for high data rate services. The paper addresses power allocation methods for multi-operator multi-beam uplink satellite communication systems co-existing with a Ka-band terrestrial network, using cognitive radio paradigm. Such a scenario is especially challenging because of (i) the coexisting multiple SatCom operators over the cognitive band need to coordinate the use of their resources under limited inter-operator information exchange, and (ii) nonlinear onboard high power amplifier (HPA) which leads to nonlinear interference between users and beams. In order to tackle the first challenge, we propose distributed power allocation algorithms including the standard Alternate Direction Multiplier Method (ADMM); Regarding the HPA nonlinear impairment, we propose nonlinear-aware power allocation based on Signomial Programming. The proposed solutions outperform state-of-the-art in both cases.

Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain

This paper is concerned with the blow-up of solutions to the initial boundary value problem for the wave equation with scale invariant damping term on the exterior domain, where the nonlinear terms are power nonlinearity |u|^{p} , derivative nonlinearity |u_{t}|^{p} and combined nonlinearities |u_{t}|^{p}+ |u|^{q} , respectively. Upper bound lifespan estimates of solutions to the problem are obtained by constructing suitable test functions and utilizing the test function technique. The main novelty is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems 1.1–1.3 are new.

Full Feedback Dynamic Neural Network with Exogenous Inputs for Dynamic Data‐Driven Modeling in Nonlinear Dynamic Power Systems

AbstractDynamic neural networks (DNNs) are widely used in data‐driven modeling of nonlinear control systems. Due to the complexity of the actual operating nonlinear power systems, rigorous dynamic models are always unknown. DNNs can focus on methods that only use input and output information to establish accurate dynamic models and reduce noise in measured data, which is called data‐driven modeling. The core of the DNN is the feedback with memory function. This paper analyzes the traditional Elman neural network (ENN) and nonlinear auto‐regression with exogenous input (NARX) neural network with different structure feedback structures, and proposes a full feedback dynamic neural network (FF‐DNN) with exogenous input. Eight different kinds of neural networks (including ENN, NARX, etc.) are compared and analyzed. The eight kinds of neural networks are applied on the experimental data of the DC‐AC inverter and the power system of Zhejiang Juchuang Smart Technology Company Park in Wenzhou. The experimental results are used to compare the performance of the data‐driven models established by eight different kinds of neural networks under different noise conditions, verify the robustness and generalization performance of dynamic data‐driven modeling based on FF‐DNN, and demonstrate the feasibility and effectiveness of FF‐DNN in actual power systems. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Deep Neural Network for the Behavioral Modeling of Memory Effects and Supply Dependency on 10-W Nonlinear Power Amplifiers

In this paper, a deep neural network (DNN) model is proposed for the behavioral modeling of nonlinear power amplifiers with supply dependency. Although the conventional nonlinear model, such as the Volterra series, has high accuracy, it is not commonly implemented because of its complexity. However, with manageable complexity, the multidimensional input parameters of the proposed model ensure the modeling of the nonlinear behavior of power amplifiers with supply voltage dependency. The proposed model is trained by multi-tone signals on a 10-W power amplifier and validated by comparing the output spectrum and the third-order intermodulation (IMD3) of the model versus the measured data. The output spectrum shows less than 0.38 dB of error over a bandwidth of 10 MHz and input power from 11 dBm to 17 dBm, and the IMD3 error is less than 0.1 dB over the output power range.

A robust autonomous sliding-mode control of renewable DC microgrids for decentralized power sharing considering large-signal stability

DC microgrids (MGs) are providing a pathway toward a zero-carbon-based future. The intermittent renewable energy sources (RESs) and non-linear constant power loads (CPLs) thrive in DC MGs, craving for effective coordinative control solutions to ensure the stability of DC MGs. In this paper, a robust autonomous sliding mode control (SMC) scheme is proposed for achieving a globally stable and decentralized power sharing operation of multiple dispatchable units (DUs) in CPL-integrated DC MGs. Firstly, by using the high-order finite-time observer (HOFTO) technique, the disturbances, such as the power coupling and parameter uncertainties between different DU-interfaced converters, are self-eliminated within a finite time without any output current sensor and communication link. Secondly, a decentralized control scheme synthesizing the robust SMC and droop control algorithm is proposed to achieve proportional power sharing among paralleled DUs and precise DC bus voltage regulation. The proposed control guarantees the global system’s large-signal stability by ensuring the local stability of an individual converter, offering a simple yet effective stable coordinative solution. Finally, simulation and experimental results verify the effectiveness of the proposed strategy.

Numerical study of the transverse stability of line solitons of the Zakharov–Kuznetsov equations

We present a detailed numerical study of the stability under periodic perturbations of line solitons of two-dimensional, generalized Zakharov–Kuznetsov equations with various power nonlinearities. In the L2-subcritical case, in accordance with a theorem due to Yamazaki we find a critical speed, below which the line soliton is stable. For higher velocities, the numerical results indicate an instability against the formation of lumps, solitons localized in both spatial directions. In the L2-critical and supercritical cases but subcritical for the 1D generalized Korteweg–de Vries equation), the line solitons are shown to be numerically stable for small velocities, and strongly unstable for large velocities, with a blow-up observed in finite time.

Design of an S-shaped point-absorber wave energy converter with a non-linear PTO to power the satellite-respondent buoys in the East China Sea

An S-shaped wave energy converter (SB-WEC) was designed to assist near-zero-energy oceanography. The SB-WEC comprises a non-linear mechanical power take-off (PTO) and a novel S-shaped buoy (SB) for operation in the wave climate of the National Shallow Sea Comprehensive Test Site in China. The PTO used a ball screw-based transmission system to harvest wave energy during upward and downward strokes, and its operational characteristics were validated through simulations and experimental testing. A comparative analysis was performed to select an optimal buoy shape, and tests were conducted in a lab-scale wave flume on the 3D-printed scaled buoys. Using an ultramodern algorithm, buoy scaling was performed to identify the pure shape-change effects on the heave response irrespective of their size. The optimal buoy size was evaluated, and an algorithm was developed in MATLAB Simscape to study its feasibility of running the non-linear PTO in realistic waves. A study on the tunability of the PTO using a rotary motion rectifier (RMR) suggested that the application of the proposed RMR is not suitable in waves below 0.3 Hz. During experimental tests, the PTO generated 13.5W at 0.3 Hz (realistic wave frequency) with an energy conversion efficiency above 50%. The experiments showed that under identical design and test conditions, the S-shaped buoy (SB) could achieve a 34% greater RMS heave response than the cylindrical-hemispherical buoy. A feasibility study based on MATLAB-AQWA showed that the RMS power absorption of the full-scale SB buoy was 17% higher than the input power of the PTO in irregular waves, validating the proposed buoy shape and size. The SB-WEC can reasonably power the sensors in the satellite-respondent buoys.

Wiener predistorter for nonlinear satellite downlinks

SummaryThe nonlinear power amplifier and the analogue output channel filter with nonconstant group delay add nonlinear and linear distortions to the satellite transmitted signal, respectively. Recently, there has been growing interest in using Wiener predistorters, consisting of separate nonlinear and linear components, to compensate for these distortions in the satellite downlinks. The Wiener predistorter has been shown to effectively deal with signal distortions and has lower complexity compared to other state‐of‐the‐art methods. In this paper, we argue that fully compensating the nonconstant group‐delay distortion degrades the overall performance of the Wiener predistortion systems. This is primarily due to the increased peak‐to‐average power ratio of the signal at the output of the linear predistorter. We show that the overall performance of the Wiener predistorter can be improved by undercompensating the group‐delay distortion. We propose two optimizations to address the PAPR growth problem and show using simulations that our approach leads to significant improvement in predistortion performance. Using our Wiener predistorter, the total degradation gap to the ideal limiter channel can be reduced to merely 0.34 dB for 64‐APSK modulated signals.

Dynamical chaos in nonlinear Schrödinger models with subquadratic power nonlinearity.

We devise an analytical method to deal with a class of nonlinear Schrödinger lattices with random potential and subquadratic power nonlinearity. An iteration algorithm is proposed based on the multinomial theorem, using Diophantine equationsand a mapping procedure onto a Cayley graph. Based on this algorithm, we are able to obtain several hard results pertaining to asymptotic spreading of the nonlinear field beyond a perturbation theory approach. In particular, we show that the spreading process is subdiffusive and has complex microscopic organization involving both long-time trapping phenomena on finite clusters and long-distance jumps along the lattice consistent with Lévy flights. The origin of the flights is associated with the occurrence of degenerate states in the system; the latter are found to be a characteristic of the subquadratic model. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border, above which the field can spread to long distances on a stochastic process and below which it is Anderson localized similarly to a linear field.

Natural gas consumption forecasting using an optimized Grey Bernoulli model: The case of the world’s top three natural gas consumers

The accurate and reasonable prediction of natural gas consumption is important for enhancing national energy security and alleviating the environmental problems caused by energy consumption. Starting with the traditional nonlinear grey Bernoulli model, in this paper, we expand the development coefficient a and grey action quantity b, propose a new self-adaptive time-varying grey Bernoulli prediction model, deduce the time response formula of the model, and explore the relationship between model parameters and model accuracy. Then, the nonlinear parameter and power parameter coefficient of the new model are optimized by a genetic algorithm, and the effectiveness of the model is analyzed by the natural gas consumption of China, the United States, and Russia. The results show that, compared with other traditional grey prediction models, the new model has a better simulation effect, higher prediction accuracy, and stronger applicability. Meanwhile, the model was used to forecast the natural gas consumption of China, the United States, and Russia in the period from 2022 to 2026. The prediction results show that China’s natural gas consumption will continue to steadily increase in the future, which is consistent with the global goal of adhering to the orderly development of natural gas. The prediction results can provide a theoretical basis for relevant departments to formulate relevant natural gas policies.

Probabilistic Power Flow Method for Hybrid AC/DC Grids Considering Correlation among Uncertainty Variables

For a new power system using high-penetration renewable energy, the traditional deterministic power flow analysis method cannot accurately represent the stochastic characteristics of each state variable. The aggregation of renewable energy with different meteorological characteristics in the AC/DC interconnected grid significantly increases the difficulty of establishing a steady-state model. Therefore, this study proposes an improved Latin hypercube sampling algorithm using the van der Waerden scores and diffusion kernel density estimation to overcome the limitations of a priori assumption on probability distributions in uncertainty modeling and to retain the correlations among random variables in the sampling data. Interconnected grids are constructed with IEEE 9-bus and IEEE 14-bus and modified with IEEE 57-bus to describe common application cases of aggregated renewable energy. On this basis, the approximation errors of the proposed probabilistic power flow algorithm to the statistical characteristics of the power parameters are evaluated by setting the Nataf algorithm and the Latin hypercube algorithm using adaptive kernel density estimation as the control group. The results show that the improved Latin hypercube sampling algorithm can exhibit high computational accuracy and strong adaptability, both in severe operating scenarios with large amplitude of load fluctuations and with nonlinear power balance equations incorporating high dimensional random variables.

Results on the Spectral Stability of Standing Wave Solutions of the Soler Model in 1-D

We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(\langle\psi,\beta \psi\rangle_{\mathbb{C}^2}) \beta$. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form $e^{-i\omega t} \phi_0$. For the case of power nonlinearities $f(s)= s |s|^{p-1}$, $p>0$, we obtain a range of frequencies $\omega$ such that the linearized operator has no unstable eigenvalues on the axes of the complex plane. As a crucial part of the proofs, we obtain a detailed description of the spectra of the self-adjoint blocks in the linearized operator. In particular, we show that the condition $\langle\phi_0,\beta \phi_0\rangle_{\mathbb{C}^2} > 0$ characterizes groundstates analogously to the Schr\"odinger case.

Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming

Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is.

Hi-COLA: fast, approximate simulations of structure formation in Horndeski gravity

We introduce Hi-COLA, a code designed to run fast, approximate N-body simulations of non-linear structure formation in reduced Horndeski gravity. Given an input Lagrangian, Hi-COLA dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. Hence Hi-COLA is a general, adaptable, and useful tool that allows the mildly non-linear regime of many Horndeski theories to be investigated for the first time, at low computational cost. In this work, we first describe the screening approximations and simulation setup of Hi-COLA for theories with Vainshtein screening. We validate the code against traditional N-body simulations for cubic Galileon gravity, finding 2.5% agreement up to k max = 1.2 h/Mpc. To demonstrate the flexibility of Hi-COLA, we additionally run the first simulations of an extended shift-symmetric gravity theory. We use the consistency and modularity of Hi-COLA to dissect how the modified background, linear growth, and screened fifth force all contribute to departures from ΛCDM in the non-linear matter power spectrum. Hi-COLA can be found at https://github.com/Hi-COLACode/Hi-COLA.

Mitigating Impact of High Power Ramp Rates in Utility Grid Integrated Wind–Solar System Using an RLMAT Adaptive Control Strategy

With the unremitting progress in renewable energy based systems into a sizeable contributor in global energy mix, the need to address challenges associated with their inherent power variability has also risen. The high power-ramp rates experienced during sudden wind gusts and cloud passing are known to impact the security of the power grid, especially in remotely-located wind-solar systems. These challenges are further intensified with sudden connection/disconnection of large local loads in the system, which demand power at a high ramp rate. This work deals with the use of a coordinated control strategy for power converters, to limit the grid power-ramp rate during the aforementioned high power-ramp events (HPREs). The deficit power during HPREs is absorbed by the energy storage system (ESS). The reference currents for ramp rate limiting control are computed using a robust least mean absolute third (RLMAT) adaptive filter. The RLMAT filter further assists in improving the grid currents power quality in presence of nonlinear, unbalanced and poor power factor local loads in the system. The effectiveness of the control strategy is evaluated through both simulation analysis and test results obtained from a laboratory-scale prototype.